Interdiffusion and Kirkendall Effect in Doped BaTiO3–BaZrO3 Perovskites: Effect of Vacancy Supersaturation

Abstract

Interdiffusion in Sc‐doped and Ta‐doped BaTiO3‐BaZrO3 perovskites was examined, both theoretically and experimentally. Analytical expressions for the lattice velocity, v, and the interdiffusion coefficient,D̃, were obtained. The v and the D̃ were numerically evaluated as a function of dopant type (trivalent‐acceptor or pentavalent‐donor) and concentration using literature values of oxygen vacancy diffusivity, DVO, the A‐site vacancy diffusivity, DVA, and assumed values for the B‐site vacancy diffusivities, DVB and DVB′. Regardless of the chosen values of DVB and DVB′, the calculated D̃ increased with the Ta concentration and decreased with the Sc concentration. The dependence (shape) of the calculated v vs dopant type and concentration, however, was a function of the magnitudes of DVA and DVB. For DVA < (DVB, DVB′) < DVO, the calculated v exhibited a maximum at ∼0.8% acceptor dopant. Diffusion couples in the BaTiO3‐BaZrO3 system doped with either Sc (acceptor) or Ta (donor) were annealed in air over a temperature range between 1300° and 1500°C. Extensive Kirkendall porosity was observed in several samples. The measured porosity vs dopant concentration (acceptor/donor) trace was similar to that of calculated v vs dopant concentration (acceptor/donor). However, the measured D̃ vs dopant concentration (acceptor/donor) was not in accord with the calculations. This difference is attributed to a nonequilibrium vacancy supersaturation and the accompanying porosity formation. To obtain further evidence of the deviation from equilibrium, experiments were also conducted on both coarse‐grained and fine‐grained samples. The coarse‐grained samples, which are expected to have fewer vacancy sinks and sources, exhibited greater Kirkendall porosity and greater D̃ values compared to the fine‐grained samples, consistent with a greater deviation from equilibrium.